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The Relationship between Temperature and Velocity in Turbulent Boundary Layers with Injection

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Recent Advances in the Aerospace Sciences
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Abstract

The relationship between temperature and velocity in turbulent boundary layers has been of considerable interest ever since the publication of the pioneering papers by Crocco on the corresponding results in laminar flow. As a result a number of authors have derived a simple algebraic form for the relation, the Crocco relation. This simple form has been found to be in close agreement with experimental results over a wide range of conditions although there are a large number of inexplicable discrepancies. This paper reviews the various derivations of the Crocco relation to see if the approximations used break down under certain circumstances. In fact no obvious reasons for the discrepancies have been found. However, it has been possible to extend some of the derivations to boundary-layer flows over porous surfaces and the results are found to be in good agreement with experiment, even in highly nonequilibrium layers, for example, in the boundary layer downstream of a porous surface.

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References

  1. L. Crocco, Su di un valor massimo del coefficiente di trasmissione del calore da una lamina piana a un fluido scorrente, L’Aerotecnica 12, 181–197 (1932).

    Google Scholar 

  2. L. Crocco, Lo strato limite laminare nei gas, Monografie Scientifiche d’Aeronautica, No. 6 (1947).

    Google Scholar 

  3. H. H. Fernholz and P. J. Finley, A critical compilation of compressible boundary layer data, AGARD AG-223 (1977).

    Google Scholar 

  4. H. H. Fernholz and P. J. Finley, A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers, AGARD AG-253 (1980).

    Google Scholar 

  5. H. H. Fernholz and P. J. Finley, A further compilation of compressible boundary layer data with a survey of turbulence data, AGARD AG-263 (1981).

    Google Scholar 

  6. E. R. Van Driest, in: 50 Jahre Grenzschichtforschung, pp. 257-271, Friedr. Vieweg & Sohn, Braunschweig (1955).

    Google Scholar 

  7. A. Walz, Compressible turbulent boundary layers with heat transfer and pressure gradient in the flow direction, J. Res. Natl. Bur. Stand., Sect. B 63, 53–70 (1959).

    MathSciNet  MATH  Google Scholar 

  8. D. A. Spence, Velocity and enthalpy distributions in the compressible turbulent boundary layer on a flat plate, J. Fluid Mech. 8, 368–387 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Howarth, Concerning the effects of compressibility on laminar boundary layers and their separation, Proc. R. Soc. London 194, 16–41 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  10. D. L. Whitfield and M. D. High, Velocity-temperature relations for turbulent boundary layers with non unity Prandtl numbers, AIAA J. 15, 431–434 (1977).

    Article  Google Scholar 

  11. A. J. Laderman, Total temperature-velocity relation in turbulent compressible boundary layers, Int. J. Heat Mass Transfer 24, 1990–1992 (1981).

    Article  Google Scholar 

  12. L. C. Squire, Further experimental investigations of compressible turbulent boundary layers with air injection, ARC R & M 3627 (1970).

    Google Scholar 

  13. L. C. Squire, Eddy viscosity distributions in compressible turbulent boundary layers with injection, Aeronaut. Q. 23, 169–182 (1971).

    Google Scholar 

  14. L. O. F. Jeromin, The status of research in turbulent boundary layers with fluid injection, Prog. Aeronaut. Sci. 10, 65–189 (1970).

    Article  Google Scholar 

  15. L. C. Squire and V. K. Verma, The calculation of compressible turbulent boundary layers with fluid injection, ARC Current Paper No. 1265 (1973).

    Google Scholar 

  16. B. M. Leadon and C. J. Scott, Transpiration cooling experiments in a turbulent boundary layer at M = 3, J. Aeronaut. Sci. 23, 798–799 (1956).

    Google Scholar 

  17. E. R. Bartle and B. M. Leadon, Experimental evaluation of heat transfer with transpiration cooling in a turbulent boundary layer at M = 3.2, J. Aeronaut. Sci. 27, 78–80 (1960).

    Google Scholar 

  18. E. J. Hopkins, Charts for predicting turbulent skin friction from Van Driest method (II), NASA TN D-6945 (1972).

    Google Scholar 

  19. G. D. Thomas, Compressible turbulent boundary layers with combined air injection and pressure qradient, ARC R & M 3779 (1976).

    Google Scholar 

  20. P. G. Marriott, Compressible turbulent boundary layers with discontinuous air transpiration: An experimental and theoretical investigation, ARC R & M 3780 (1977).

    Google Scholar 

  21. J. E. Danberg, Characteristics of the turbulent boundary layer with heat and mass transfer at M = 6.7, NOLTR 64-99 (1964) [see also NOLTR 67-6 (1967)].

    Google Scholar 

  22. L. Crocco, Transformations of the compressible turbulent boundary layer with heat exchange, AIAA J. 1, 2723–2731 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  23. D. I. A. Dunbar and L. C. Squire, Correlations of concentration, temperature and velocity profiles in compressible turbulent boundary layers with foreign gas injection, Int. J. Heat Mass Transfer 14, 27–40 (1971).

    Article  Google Scholar 

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© 1985 Plenum Press, New York

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Squire, L.C. (1985). The Relationship between Temperature and Velocity in Turbulent Boundary Layers with Injection. In: Casci, C., Bruno, C. (eds) Recent Advances in the Aerospace Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-4298-4_9

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  • DOI: https://doi.org/10.1007/978-1-4684-4298-4_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-4300-4

  • Online ISBN: 978-1-4684-4298-4

  • eBook Packages: Springer Book Archive

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